Final answer:
It will take approximately 2.23 seconds for an 870 kg car with a power output of 44.0 hp to accelerate to 13.0 m/s from rest, assuming no friction is involved.
Step-by-step explanation:
To calculate how long it will take an 870 kg car with a useful power output of 44.0 hp to reach a speed of 13.0 m/s, neglecting friction, we will use the work-energy principle. First, convert horsepower to watts: 44.0 hp × 746 W/hp = 32824 W. The car's kinetic energy (KE) at 13.0 m/s is given by the equation KE = 0.5 × m × v^2, which is 0.5 × 870 kg × (13.0 m/s)^2 = 73,305 J.
Now, power (P) is the rate of doing work, so we have P = W/t, where W is work done, which is equivalent to the kinetic energy here, and t is time. Therefore, t = W/P. Plugging in the values gives us t = 73,305 J / 32824 W ≈ 2.23 s. This is the time it will take the car to reach 13.0 m/s from rest, assuming no friction.